The 18-year-old German-American has signed a deal that will keep him with the German champions until 2017.
Green has been playing with Bayern Munich's reserve team in the Baravian section of the Regionalliga, and he currently leads that division in scoring with 15 goals in 17 appearances.
The contract ties Green to the club through June 2017 and ensures no other teams can make a swoop for the forward.
USA coach Jurgen Klinsmann confirmed he is interested in bringing Green into the American team but said he would not be called into the team's November camp for friendlies against Scotland and Austria. The player subsequently accepted a call-up to the German U-19 team but could still file a one-time switch should he decide to play for the USA instead of representing Germany.
Bayern also confirmed it has signed Austrian youth international Alessandro Schopf to a contract through 2016.